Papers

We study stochastic dynamic matching with abandonment, a fundamental model in which agents of different types arrive over time, may abandon the market while waiting, and can be matched in pairs for rewards that depend on their types. No online policy can guarantee more than $0.5$ of the omniscient benchmark, which knows all arrival and departure times. Whether this guarantee is achievable has been a central open problem, even in special cases. We resolve this problem by showing that, on every instance, a simple static priority policy, which is computable in polynomial time, earns at least $0.5$ of the omniscient benchmark. This establishes that the optimal competitive ratio is exactly $0.5$, improving the previous best guarantee of 0.192 for the general model [Li et al. 2026; Collina et al. 2020] Our analysis rests on a key stochastic result, which is a new lower bound on the probability that some agent from a given set of types is available. Building on this bound, we develop two approaches: a primal approach that reads the priorities from an optimal solution of a novel linear program, and a dual approach that assigns a “value” to each type, and prioritizes matches with high “surplus” (reward minus value of involved agents). These values are the unique solution of a fixed-point equation derived from linear programming duality. We also show that the two approaches are closely connected.

Deploying AI agents to combat dishonest communication is an intuitive response to deception in hybrid human-AI societies. However, the efficacy of such interventions in realistic networked settings remains unclear. We study this problem using an evolutionary game-theoretic model of the Deceiver's Game by extending it to structured networks, where agents can adopt deception, truth-telling, and investigation strategies. We introduce committed AI agents (zealots) fixed to either truth-telling or investigative strategies and conduct agent-based simulations across three network topologies. Our key findings are: (1) passive committed truth-telling agents can amplify adaptive deception by creating exploitable honest partners, whereas investigative agents increase adaptive truth-telling in the oscillatory regime; (2) intervention effects are non-monotonic in deployment density because committed agents reshape rather than simply suppress the underlying oscillatory dynamics; and (3) response peaks depend on topology, with sampled scale-free populations showing sharp low-density responses and fully connected populations requiring larger committed fractions. Overall, the results highlight the need to distinguish passive truth-telling from active investigation when using committed agents to influence networked deception dynamics.

"Security by obscurity," or the idea that hiding how a system works helps protect it from adversaries, has long been poorly regarded in the security community. Yet its intuitive appeal persists, and it has resurfaced repeatedly in industry practices and public debates over the years. The logic, on the one hand, is that open scrutiny of systems is the best way to find and respond to problems; and on the other hand, that too much openness can increase risk by giving adversaries a roadmap for attack. This isn't purely a technical question, but a human one: it's about how attackers and good-faith security researchers respond to openness in the real world. As such, security experts base their stance on decades of community experience; however, the field lacks empirical or theoretical foundations to back up these long-standing beliefs. We provide the first rigorous modeling of "security by obscurity," aiming to capture how rational actors will respond to openness or obscurity in fallible systems. We prove that in equilibrium under realistic model conditions, "obscured" systems are more likely to suffer successful attacks than "open" systems — establishing theoretical support for the longstanding received wisdom.

Large-scale strategic systems, such as maintenance workflows, cyber campaigns, and multi-agent AI pipelines, consist of many interactions whose outcomes determine which later interactions become possible, who takes part, and with what resources. We introduce game Petri nets, formalized as outcome-driven compositional game Petri nets (OCGPNs), to model and analyze such systems. Local games are attached to places of a colored Petri net, and a game-to-token interface converts each resolved game into typed tokens that enable, synchronize, or block subsequent games. For general, concurrent nets, we give an operational semantics and a structural theory based on invariants and Farkas certificates, which shows that guards can certify unreachability whereas incentive instruments can only change values. For sequential nets, the net induces a stochastic game on its game places. We prove that global equilibria are exactly collections of equilibria of local games augmented by continuation values, characterize through successor-level pivotality when downstream games change upstream behavior, and compute values place by place via a decomposition into strongly connected components, at a cost additive in local game sizes. A composition calculus based on place fusion glues certificates across subnets and summarizes downstream subnets by their entry values. Two running examples, a maintenance workflow and an intrusion campaign derived from multi-resolution cyber-defense games, illustrate the theory, including the composition of a newly discovered attack scenario with an existing campaign.

Spatial public goods models show that prescribed movement toward richer locations can generate spatial patterns. We ask how such patterns emerge when agents learn where to move and how learning rates shape their consequences for collective welfare. Fixed populations of cooperators and defectors independently learn movement policies using tabular Q-learning and local observations. Cooperator learning generates clusters around resource peaks, while co-adaptation changes their strength and motion. At a fixed training budget, the largest welfare losses occur when cooperators learn at high rates and defectors at low rates. In part of this regime, learned policies also generate traveling bands supported by a shared directional preference. The conditions supporting travel change with further training, so these patterns reflect training history rather than an established asymptotic outcome. Across the tested learning-rate conditions with cooperator learning, mean collective welfare falls below random movement because increased crowding outweighs gains in resource benefit. Charging agents for the crowding they impose on others during learning recovers much of the welfare loss in the tested conditions. These results connect learning rates to the emergence and welfare costs of spatial organization driven by individual rewards.

Software-Defined Networking (SDN) is emerging as a promis- ing technology for EV Charging infrastructure (EVCI) since it enables flexible, programmable control of EVCI networks, yet its security gain to EVCI remains underexplored. SDN-enabled EVCI faces an increas- ing number of cyber threats arising from the convergence of IT and OT components; in particular, low-rate Denial-of-Service (DoS) attacks. Ear- lier works identify a trend toward low-rate attacks in OT networks that may exhaust SDN switch flow tables and which can result in disabling the entire charging sites without triggering volume-based defenses. In this paper, we propose CS-SHIELD, a Moving Target Defense mecha- nism for SDN-enabled EVCI communication. We showcase the imple- mentation of the proposed mechanism that detects malicious flow table rules via cross-layer identity verification and responds by reassigning virtual IP addresses to all active chargers. Experiments on an emulated SDN testbed with a real charging protocol implementation demonstrate that CS-SHIELD maintains full site availability under attack, responds quickly, adds only a negligible delay under normal conditions. The reas- signing (shuffle) approach at each reaction makes the earlier reconnais- sance knowledge by the attacker rendered worthless.

In the graph model for conflict resolution (GMCR), a decision maker (DM) either moves the conflict to another state or does nothing. The basic definitions leave inaction implicit, so every action that leaves the state unchanged is treated as doing nothing. Yet announcements, exercises, leaks and selective disclosures are neither moves nor inaction: they leave the state unchanged but change what other DMs believe about which moves are available and which moves others would want to make. We introduce such state-preserving actions by augmenting states with the DMs' epistemic states: a physical move changes the physical state, a state-preserving action changes only the epistemic state, and inaction is the absence of a transition. Actions generate evidence through observer-specific interpretation maps. Building on a four-valued extension of GMCR from the author's earlier work, which separates evidence for and against, we show that evidence for a move can only enable perceived moves and evidence against can only disable them, that two of the four reduction operators ignore one kind of evidence, and that contradictory assessments are absorbing under monotone accumulation. With the monotonicity of stability in move sets, this fixes the direction in which any action moves a DM's stability judgements and characterizes when actions can enable provocation or deterrence. Capability assessments affect all sanction-based stability concepts, and on the DM's own side also Nash stability, whereas intention assessments affect only sequential stability. Hedging between two candidate types weakly expands or shrinks an observer's sequentially stable set according to how it reads contradiction. In the 1995 DVD format negotiation, general metarationality cannot distinguish its phases, since the computer industry group could always sanction; sequential stability, which asks whether it would, can.

We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium.

Botnets represent the backbone of most modern cybersecurity attacks through which botmasters deploy distributed denial of service and advanced persistent threats against legitimate computer networks. In this paper we introduce the Host Attack Graph model and propose two botnet propagation strategies which we study across network topologies, target selection, and attack strategies together with their effectiveness in time. While strategy and botnet size are important for propagation, our study and simulations show that network topology and target selection should not be easily discarded. Implementation and benchmarks are available at https://codeberg.org/AndreiN/HAGP.

Prediction aggregation aims to combine information from multiple predictors into a more informative one. We study this question in the setting of calibrated predictors, where each prediction must equal the conditional expectation of the quantity being predicted given the predictor's signal. Given several calibrated input predictors and the feature distribution, but not the underlying Bayes probabilities, we ask when one can construct refined calibrated predictors that preserve the information in the original predictors and cannot be further refined using the available information. We formulate calibrated predictors as signaling schemes and define refinement through feature-independent garblings: a predictor refines another if its signal can simulate the other's signal. Constructibility is characterized through observable linear information: each signal corresponds to a vector over the feature space, and a new signal is constructible exactly when its vector lies in the linear span of the input signal vectors. Under this formulation, we establish a sharp algorithmic picture. For deterministic output predictors, bilateral refinement admits a polynomial-time algorithm based on a bipartite graph between the two input signal partitions, while refinement with an arbitrary number of input predictors is $\mathsf{NP}$-hard. In contrast, when randomized output predictors are allowed, we give a polynomial-time algorithm for any number of input predictors by decomposing constructible signal vectors into extreme rays of the associated polyhedral cone.

We establish near-optimal regret bounds for budget-constrained online learning against arbitrary classes of budget-pacing experts in the adversarial setting. In particular, given any class of $F$ experts and a candidate budget pacing schedule, we provide a full-information algorithm which obtains regret $O(D \sqrt{\log F}+ \sqrt{T\log F})$ against all experts whose cumulative spending stays within distance $D$ of this schedule, matching lower bounds established by Braverman et al. (2025). We additionally show that our technique extends to various problems in online resource allocation, where the learner gets to see the rewards and costs of the current options available to them, and establish $O(D\sqrt{\log F})$ regret bounds when fractional allocation is allowed. This is the first algorithm we are aware of which can achieve $o(\sqrt{T})$ guarantees for such tasks.

We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a polynomial-time algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate algorithms under different parameter restrictions. Exact polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these algorithms satisfy DSIC and ex-post individual rationality.

We study worst-case VCG redistribution mechanism design for the public project problem, where n agents decide whether to build a non-excludable public project and the designer chooses a Groves term that returns as much of the VCG payment as possible without running a deficit. The objective is the worst-case efficiency ratio, the worst-case ratio between the agents' total utility and the first-best total utility. Prior work showed that this ratio can approach 1 as n grows only under a bounded precision assumption, that all types are rational numbers with a common bounded denominator. The assumption is stronger than it looks: it confines the difficult profiles to those in which all but a bounded number of agents report zero, and an agent who reports zero knows the total exactly. Without it, the best known guarantee tends to 1/2. We remove the assumption. We construct a deterministic, anonymous, strategy-proof, and non-deficit mechanism for arbitrary real types in [0,1] whose worst-case efficiency ratio is 1-O(1/log log n). The construction estimates the shortfall of the reported total below the project cost by filling in each agent's missing report with a resampled one, then estimates the error of that estimate, then the error of the error, and so on. After m rounds the aggregate error is at most 1/Hm mean reports, where Hm is the mth harmonic number. The proof of this bound is the heart of the paper and, unusually for a result about payments, uses complex analysis: a trigonometric representation of the shortfall function together with the Poisson-Jensen inequality for bounded analytic functions in the upper half plane.

Motivated by social services where consumers pay with non-transferable ordeals, we study mechanisms that maximize consumer utility for multiple unit-demand buyers and heterogeneous items whose values are drawn independently from known prior distributions. Prior work in utility maximization approximates social welfare and shows that the gap between optimal utility and social welfare is logarithmic. We resolve the question of whether simple mechanisms can guarantee a constant-factor approximation to optimal utility itself. Our mechanisms achieve a $(5.67+\varepsilon)$-approximation for general independent values, improving to $2e/(e-1)<3.164$ when values are i.i.d. Each buyer chooses their favorite option from posted item prices or free item lotteries, and contention resolution determines which buyers' requests are served; this is BIC, ex-post individually rational, and computable in polynomial time. Our main technical contribution is a general upper bound on the optimal ex-ante-constrained utility that separates the contributions captured by posted prices and free lotteries. These results establish a utility counterpart to the theory of simple, approximately revenue-optimal mechanisms.

The Guaranteed Utility Mechanism (GUM) was introduced to implement efficiency in Guaranteed Utility Equilibrium (GUE) in dynamic social choice problems. We show that this mechanism also has a previously unknown connection to risk minimization. Fixing an efficient decision policy, we study variance-minimizing budget-balanced transfer rules in the class of GUE-implementations of truthful reporting. A symmetrized version of GUM (sym-GUM) minimizes the sum of the agents' utility variances under truthful reporting when there is no public state. When a public state is present, a slight modification of this rule yields the minimizer for the same objective. Sym-GUM, however, does not minimize transfer risk. The minimizer for that problem is instead the symmetrized version of a closely related GUM-like transfer rule. In both problems, the minimizing truthful total transfers are unique up to agent-specific constants summing to zero and events of probability zero.

We study proportional fairness in graphical resource allocation, where agents are vertices, indivisible items are edges, and each item must be allocated to one of its two endpoints. It has been proved that PROP1 orientations always exist and PROPx orientations may not, but it has remained open whether the intermediate relaxations PROPm and PROPavg (both can be satisfied without graphical constraints) can always be satisfied. In this paper, we resolve this gap. We prove that PROPm orientations always exist for goods on multigraphs and can be computed efficiently. The guarantee extends to chores and a mixture of goods and chores. In sharp contrast, we show that PROPavg orientations need not exist, even for simple graphs with binary valuations, and that deciding their existence is NP-complete. We further quantify the efficiency loss of PROPm: for goods, the price of PROPm is exactly $2$, which is one of the few settings where a constant bound on the price of fairness can be obtained. We complement these results with hardness results for welfare optimization under PROPm and for the existence of orientations that are simultaneously PROPm and Pareto optimal.

We consider the problem of parameter selection for EIP-1559, a widely used gas pricing mechanism for blockchains. As opposed to previous work, we aim to achieve economic security, where the chosen parameters guarantee a lower bound on total collected gas fees whenever usage over a given time window exceeds a specified threshold. This bound can be set prohibitively high, thereby economically deterring usage above a desired level. Such guarantees are particularly relevant to long-term objectives such as limiting state growth. We apply our approach to the pure exponential version of EIP-1559 which Ethereum uses and to a variant used by Robinhood Chain and Arbitrum. To achieve economic security, we first characterize the revenue-minimizing gas-usage distribution for the exponential version and for the other variant we construct a distribution whose associated fee revenue provably approximates the minimum. Using these results, we then demonstrate how to set economically secure mechanism parameters for both variants and we discuss the associated tradeoffs.

In perfect-information two-player stochastic games, the notions of Blackwell and sensitive optimality provide generalizations of the classical mean-payoff optimality and discount optimality criteria to account for more farsighted preferences. We provide bounds on the Blackwell threshold $\alpha_{\sf bw}$ and the $d$-sensitive thresholds $\alpha_{\sf d}$, defined as the smallest discount factors above which discount optimal policies coincide with Blackwell optimal policies and $d$-sensitive optimal policies respectively. Our refined bounds improve upon prior work by focusing on “reduced” families of polynomials and, crucially, our bounds are tight in terms of controlling the degrees and heights of the minimal polynomials of the Blackwell thresholds. We apply classical root separation based on Mahler's and Cauchy's bounds to our reduced families to derive the strongest upper and lower bounds on $\alpha_{\sf bw}$ in the literature, and we are the first to obtain bounds on $\alpha_{\sf d}$ in the multichain stochastic setting.

We study the minimum monetary subsidy required for exact envy-freeness in allocating $m_n$ indivisible goods to $n$ agents. Valuations are additive, item values are i.i.d. from a distribution on $[0,1]$ with density bounded above and away from zero, and all agents value money equally. We consider $n\to\infty$ with $m_n=qn+r_n$, where $q\ge0$ is a fixed integer and $0\le r_n<n$. For the nonzero-remainder case where $1\le r_n<n$, we give a cubic-time algorithm based on a maximum-weight matching of balanced bundles and complementary dual prices. It returns an envy-free outcome for every instance. Under the random model, both its payment and the unrestricted minimum are $n-r_n+o_p(n)$ for $q\ge1$. When $q=0$ and $r_n/n$ converges to a limit below one, the error term improves to $O_p(1)$. For exact divisibility, where $r_n=0$, prior work gives zero subsidy with high probability for $q\ge2$. The square case $q=1$ is exceptional. Its minimum subsidy is $\Theta_p(\log n)$ and, with high probability, equals the optimum over allocations in which every agent receives exactly one good. This restricted optimum can be computed in cubic time using a maximum-weight perfect matching and all-pairs shortest paths. Together, these results provide a unified asymptotic characterization of the minimum subsidy.

We study a sequential pricing problem in which a seller jointly posts a price and an advertisement generated by a large language model (LLM). The seller aims to maximize revenue under an unknown product demand that depends on both decisions, while observing only whether each offer leads to a purchase. We propose an online actor-critic algorithm that combines low-rank adaptation (LoRA) of a pretrained LLM with a demand model fitted to available data. At each round, the actor generates an advertisement, and the critic estimates purchase probabilities to guide price selection. Then, the resulting feedback is used to update both the actor and the critic, with the critic's revenue estimates providing a baseline for policy gradient updates of the actor. To evaluate our approach, we develop an evaluation framework with three synthetic demand models and a demand simulator built from real-world marketplace data. Finally, we compare our algorithm with benchmarks that do not jointly optimize price selection and advertisement generation, achieving expected revenue gains over the reference policy of 5.69%, 5.18% and 55.96% under the three synthetic demand models and 5.81% under the marketplace simulator.

We study temporal fair division with indivisible goods that arrive sequentially and must be allocated irrevocably. In contrast to the usual online model, we assume that valuations and future arrivals are known in advance, and ask how unfairness evolves during the process. We introduce cumulative maximum envy: the sum, over all rounds, of the maximum pairwise envy at that round. Equivalently, this is the area under the worst-envy curve, and it captures both the magnitude and the duration of envy. For a fixed arrival order, we show that the corresponding decision problem is strongly NP-complete and that minimizing this objective admits no constant-factor approximation unless P = NP, even under identical valuations and even under binary valuations. We complement these hardness results with a dynamic program that gives pseudopolynomial-time solvability for a constant number of agents, polynomial-time algorithms in further restricted settings, and an FPTAS for fixed $n$ under identical integer valuations. We then study a sequencing variant where the algorithm may choose the arrival order. This variant remains NP-complete even for two agents with identical valuations; however, a simple greedy algorithm achieves a $3/2$-approximation for $n=2$ agents, an $n/(n-1)$-approximation for any number of agents, and an additive guarantee depending on the maximum value of any good.

We study online learning in market making, where, at each round, a market maker posts bid and ask prices before observing the market price and the private valuation of an incoming trader. In this setting, Maran et al. 2026 introduce a feedback model motivated by limit order books, in which the trader's valuation is revealed only if no transaction occurs. Assuming that trader valuations are drawn i.i.d. from an unknown distribution while market prices are chosen adversarially, they establish an expected regret bound of $\widetilde{\mathcal{O}}(T^{2/3})$. In this work, we improve upon this guarantee by establishing a high-probability regret bound of $\widetilde{\mathcal{O}}(\sqrt{T})$. As a warm-up, we first consider the full-feedback setting. We introduce a discretization of the bid-ask space based on two coupled grids and combine it with Hedge to achieve the desired regret rate. Building on these ideas, we then address the substantially weaker feedback induced by a limit order book and develop an algorithm that achieves the same guarantee. Finally, we investigate the limits of learnability in fully adversarial environments, where the valuations may vary arbitrarily as well. Perhaps surprisingly, we show that when both market prices and trader valuations are chosen adversarially, sublinear regret is impossible even under full feedback, thereby motivating our stochastic assumption on the valuations.

When an envy-free allocation of indivisible goods does not exist, monetary transfers can restore envy-freeness. Existing work on fair division with subsidies, however, typically assumes that these payments are provided by an external source, an assumption that may be unrealistic in many applications. We address this limitation by allowing only monetary transfers between agents, with each agent's payments constrained by their individual budget. We show that while it is polynomial-time tractable to determine whether a given allocation can be made envy-free by payments under individual budgets, the general problem of computing such an allocation from scratch is NP-hard, even when agents have relatively large budgets. Motivated by this intractability, we conduct a parameterized complexity analysis, establishing fixed-parameter tractability with respect to the number of goods or to the joint parameter number of agents and good types, and we provide efficient algorithms in several special cases. For explicitly listed items, our type-based algorithm answers the envy-freeness part of an open question of T. T. Nguyen and J. Rothe, "Complexity Results and Exact Algorithms for Fair Division of Indivisible Items: A Survey."

Calibrated uncertainty quantification is essential to ensuring AI agents are trustworthy and reliable. However, when agents seek to maximize user engagement or revenue, confidence reports may be strategically distorted, detracting from their informativeness. We formalize this problem in the Confidence Game: a repeated signaling game with imperfect monitoring in which an agent of unknown honesty and ability reports its confidence, and a user decides whether to delegate the task or complete it herself. The agent manages the tradeoff between manipulating signals and maintaining its reputation. We characterize the Markov Perfect Bayesian Equilibria of the two-period game and show that honest reporting is not an equilibrium, inflation is the unique best response once the agent is sufficiently myopic, and under-reporting requires that the user believe honesty to be a minority. We then place an LLM in the agent role, supplying it with its true probability of success so that any gap between what it knows and what it reports is attributable to incentives rather than to miscalibration. The model claims high confidence on 56% of tasks it has been told it will probably fail. This persists on real tasks, where it must estimate its own accuracy and causes miscalibration to increase while the agent's signal becomes less informative. Furthermore, we find that the LLM agent's decisions are coherent, but it systematically underestimates both how likely the user is to delegate and how secure its reputation is, resulting in less extreme behavior. Pricing the agent's reporting rule, we find that it destroys 68% of the gains from delegation, of which 71% is information the report no longer carries and no amount of user sophistication recovers. Overall, we establish confidence reporting under delegation as a strategic problem and provide a tractable basis for modeling, analyzing, and testing agent behavior.

Recent advances in mean-field games and its multi-population variants enable large-scale heterogeneous multi-agent systems to be modeled through representative agents and their associated mean-field distributions. However, existing approaches do not explicitly account for uncertainty in the behavior of other populations. To this end, we introduce a new paradigm: risk-averse multi-population mean-field games, where each population optimizes a worst-case expected reward over dynamically feasible ambiguity sets of mean-field flows of a subset of the other populations. Employing an occupation-measure formulation along with tools from set-valued analysis, we establish, under mild assumptions, several theoretical properties of the multi-population game, including the geometric properties of the ambiguity sets and the existence of a novel risk-averse multi-population mean-field equilibrium. Further, we derive contractivity results of the fixed-point operator under entropy regularization and show that it can be utilized to learn the equilibrium. Finally, we propose a risk-averse fictitious-play scheme and show that exploitability decays to zero, despite the additional nonlinearity introduced by the worst-case objective. We report several numerical experiments to illustrate convergence and risk-averse behavior.

For the online combinatorial allocation problem with subadditive valuations, Correa and Cristi (STOC 2023) proved the existence of a $6$-competitive online algorithm, improving on the previous best $O(\log\!\log m)$-competitive online algorithm due to Dütting, Kesselheim, and Lucier (FOCS 2020), where $m$ is the number of items. However, Correa and Cristi's result is existential, and it was left open whether a constant competitive ratio is attainable via an efficient online algorithm that uses a polynomial number of demand oracle queries. In this work, we answer this affirmatively, giving an expected-polynomial-time $(6 + \epsilon)$-competitive online algorithm for any constant $\epsilon > 0$. Our techniques also recover, in the offline setting, the $(2 + \epsilon)$-approximation result of Feige (STOC, 2006). Finally, when the buyers' valuations are drawn from identical distributions, we exploit symmetry to obtain an improved $(60/11+\epsilon)$-competitive algorithm. Starting with the natural configuration LP relaxation for the problem, our main technical contribution is a recursive Bundle Score Generator (BSG) that resolves item conflicts by assigning correlated scores to the items requested by each buyer. Unlike the Random Score Generator whose existence is shown by Correa and Cristi, our BSG is efficiently computable in expected polynomial time. Moreover, it satisfies a stochastic dominance property that is sufficient to recover both Feige's offline result and Correa and Cristi's online result.

It is known that completeness of the coalitional ($C$-)desirability relation in a simple game does not imply the existence of a weighted-majority representation. We show that weightedness is implied in an approximate sense. Call an $n$-player simple game $\varepsilon$-weighted if, for some weight vector in the $(n-1)$-simplex, any losing coalition weight exceeds any winning coalition weight by at most $\varepsilon$; let $\varepsilon^{\ast}$ be the smallest such $\varepsilon$. We establish an upper bound on $\varepsilon^{\ast}$ in a general $C$-complete game, and deduce that, if all classes of equally desirable players become large asymptotically but the number of classes is bounded, then $\varepsilon^{\ast}=O(1/n_{\min})$ for the minimal player class size $n_{\min}$, and the bound is tight. Importantly, the minimal attainable fraction $\delta$ of coalitions mislabeled by a weighting rule also tends to $0$ when $n_{\min}\rightarrow\infty$ and the number of player classes is bounded, with $\delta=O(1/\sqrt{n_{\min}})$.

We show that fictitious play can converge at arbitrarily slow polynomial rates in two-player zero-sum games. For every integer $k \ge 2$, we construct a payoff matrix with $(k+1)^2 - 5$ actions per player for which the duality gap of the empirical strategies decays as $\Theta(t^{-1/k})$ after $t$ steps. The family starts from the standard rock-paper-scissors matrix, with each higher-order game constructed recursively from the preceding one. After a prescribed common initial action, every subsequent best response under fictitious play is unique. For $k \ge 3$, these games give counterexamples to Karlin's conjectured $O(t^{-1/2})$ convergence rate, and they extend the recent $\Theta(t^{-1/3})$ construction of Wang (2025) to arbitrarily slow polynomial rates.

We study online profit maximization in multilateral trade, a setting that generalizes both dynamic pricing and bilateral trade. At each round, an intermediary posts prices to buyers and offers payments to sellers; trade occurs only if every agent accepts. We consider valuations drawn from an unknown joint distribution, allowing arbitrary correlation across agents, under the assumption that each agent's marginal valuation distribution has unknown support of size at most $K$. For constant dimension $d$, we design an algorithm with regret $\widetilde O(\sqrt{K^dT})$. This extends optimal support-dependent guarantees for one-dimensional dynamic pricing to the multidimensional setting of multilateral trade. At the core of our approach is a normalized zooming procedure that adapts to the local probability of trade, avoiding the excessive refinement of nearly flat regions that can arise with standard zooming.

A planner in a network of strategic agents faces three entangled challenges: the optimum depends on agents' private information, queried agents may misreport to steer the outcome, and exact computation does not scale. We study these challenges in multi-activity network games with heterogeneous private technologies, in which the planner sets non-discriminatory prices. We show that the optimal prices admit a centrality-based decomposition of the welfare kernel: each agent's contribution scales with its squared centrality in a network reweighted by agents' preferences across activities. This decomposition motivates Poll, a polling algorithm in which the planner samples one agent per round, walks briefly through the agent's neighborhood, and updates the price from a local report. From the same decomposition flow three forms of efficiency: computationally, Poll uses significantly fewer operations than exact computation and other distributed methods, requiring up to three orders of magnitude less communication on a real-world network with over 300,000 agents; statistically, its query complexity scales with topology and preference heterogeneity rather than explicitly with population size; and economically, it converges to welfare-maximizing prices while admitting behavior-specific implementations that induce truthful reports and detect adversarial deviations.